Chapter 14 Appendix – Pingouin for Repeated-Measures and Mixed ANOVA

In Chapter 14 you learned how to:

  • design a simple repeated-measures experiment (for example, Pre, Post, Followup),

  • compute the sums of squares by hand for Time, Subjects, and Residual,

  • and run a repeated-measures ANOVA using our own PyStatsV1 helper functions.

In that main chapter, the script optionally cross-checks the results with pingouin if it is installed. This appendix explains:

  • what Pingouin is and why it is useful for psychology students,

  • how to install it safely,

  • how it connects to Chapter 14 (repeated measures) and later chapters (mixed ANOVA, ANCOVA, regression, and more),

  • and a small example using the Chapter 14 synthetic dataset.

What is Pingouin?

Pingouin is an open-source statistical package written in Python 3 and built on top of NumPy and pandas. It is designed for users who want simple but comprehensive statistical functions without having to write low-level code.

Some of its capabilities include:

  • ANOVAs: multi-way between-subjects ANOVA, repeated-measures ANOVA, mixed (split-plot) ANOVA, and ANCOVA.

  • Pairwise tests and correlations: parametric and non-parametric post-hoc tests, as well as Pearson, Spearman, robust, partial, distance, and repeated-measures correlations.

  • Regression and mediation: linear and logistic regression, as well as mediation analysis with bootstrap confidence intervals.

  • Effect sizes and power: Cohen’s \(d\), partial eta-squared, confidence intervals around effects, and power analysis helpers.

  • Other tools: reliability and consistency measures, circular statistics, chi-square tests, and convenience plotting functions (for example, Q–Q plots and Bland–Altman plots).

A key advantage for teaching is that most Pingouin functions return a tidy pandas DataFrame with all the usual quantities in one place: test statistic, degrees of freedom, p-value, effect size, confidence intervals, and often a Bayes factor and power estimate.

For example, while scipy.stats.ttest_ind() returns only a t value and p-value, pingouin.ttest() returns a table with t, df, p, Cohen’s \(d\), 95% confidence intervals, power, and Bayes factor.

Installation and Dependencies

Pingouin is a Python 3 package currently tested on Python 3.8–3.11.

Its core dependencies include:

  • NumPy

  • SciPy

  • pandas

  • pandas-flavor

  • statsmodels

  • matplotlib

  • seaborn

Some additional features require:

  • scikit-learn

  • mpmath

The simplest way to install Pingouin in your PyStatsV1 environment is with pip:

pip install pingouin

If you prefer conda and the conda-forge channel:

conda install -c conda-forge pingouin

Pingouin is under active development, so it is a good idea to keep it updated:

pip install --upgrade pingouin

If you run into issues, check that your Python version and environment are compatible, and consult the Pingouin documentation and GitHub issues.

Why We Still Teach Sums of Squares

In the main body of Chapter 14 we derived the repeated-measures ANOVA from first principles:

\[SS_{\text{Total}} = SS_{\text{Subjects}} + SS_{\text{Within}}\]

and

\[SS_{\text{Within}} = SS_{\text{Time}} + SS_{\text{Residual}}.\]

This decomposition shows why repeated-measures designs are powerful: they remove stable individual differences (Subjects) from the error term (Residual), which often leads to larger F statistics for Time.

By contrast, a typical between-subjects ANOVA lumps all individual differences into a single error term. Here you see the contrast explicitly:

  • Between-subjects ANOVA (Chapter 12): error includes all person-to-person variation.

  • Repeated-measures ANOVA (Chapter 14): error is shrunk by separating out Subject variability.

Pingouin does not replace this conceptual understanding—it implements it in a robust, well-tested way and extends it to more complex designs.

How Chapter 14 Uses Pingouin

The Chapter 14 lab script (psych_ch14_repeated_measures_anova.py) implements the repeated-measures ANOVA twice:

  1. Manual / PyStatsV1 implementation

    • compute cell means, sums of squares, degrees of freedom, and F by hand,

    • print a table summarizing \(SS_{\text{Time}}\), \(SS_{\text{Subjects}}\), \(SS_{\text{Residual}}\), and \(SS_{\text{Total}}\),

    • compute a simple eta-squared style effect size for Time.

  2. Optional Pingouin cross-check

    • if pingouin is available, the script reshapes the data to long format and calls pingouin.rm_anova() with:

      • dv="stress" (the dependent variable),

      • within="time" (the repeated factor),

      • subject="id" (the participant identifier),

      • detailed=True (to get effect size and sphericity information).

    • the Pingouin output includes:

      • sum of squares, degrees of freedom, F,

      • uncorrected p-values,

      • a generalized eta-squared style effect size (ng2),

      • and an estimate of the sphericity epsilon (eps) for the Time factor.

This cross-check confirms that the hand-calculated ANOVA matches what a modern stats library reports, at least for the balanced, well-behaved designs used in our teaching examples.

Example: Using Pingouin with the Chapter 14 Dataset

After running the Chapter 14 lab script, you will have a synthetic dataset saved in:

  • data/synthetic/psych_ch14_repeated_measures_stress.csv

with one row per participant and separate columns for pre, post, and followup stress scores.

The following example shows how you could analyze this dataset directly in a Python session or Jupyter notebook using Pingouin:

import pandas as pd
import pingouin as pg

# Load the wide-format data simulated by the Chapter 14 lab
df_wide = pd.read_csv(
    "data/synthetic/psych_ch14_repeated_measures_stress.csv"
)

# Wide -> long format: one row per person per time point
df_long = df_wide.melt(
    id_vars="id",
    value_vars=["pre", "post", "followup"],
    var_name="time",
    value_name="stress",
)

# Run repeated-measures ANOVA with Pingouin
aov = pg.rm_anova(
    data=df_long,
    dv="stress",
    within="time",
    subject="id",
    detailed=True,
)

print(aov)

# Optionally, pretty-print the table
pg.print_table(aov, floatfmt=".3f")

You should see a table with:

  • a row for the Time effect (Source = "time"),

  • a row for the error term,

  • sum of squares (SS), degrees of freedom (DF), mean squares (MS), F, p-value (p-unc), generalized eta-squared (ng2), and the sphericity epsilon (eps).

If your manual ANOVA and the Pingouin ANOVA disagree substantially, check:

  • that you used the same data (no filtering or different random seeds),

  • that the design is still balanced,

  • and that the way you computed sums of squares matches the design that Pingouin assumes.

Beyond Chapter 14: Mixed ANOVA and ANCOVA

The same ideas extend to more complex designs in later chapters.

  • Mixed (split-plot) ANOVA – Chapter 17

    If you add a between-subjects factor (for example, treatment group) in addition to the repeated Time factor, you can use:

    aov_mixed = pg.mixed_anova(
    data=df_long,
    dv="stress",
    within="time",      # repeated factor
    between="group",    # between-subjects factor
    subject="id",
    effsize="np2",
    correction=False,   # or True to request a correction
)

    This produces a table with rows for the main effects of Group and Time and the Group × Time interaction, using the appropriate error terms.

  • ANCOVA – Chapter 18

    Pingouin also links naturally with statsmodels for regression-style analyses and ANCOVA, where you add a covariate (such as a pre-test score) to control for pre-existing differences between groups.

In both cases, understanding the logic of sums of squares from Chapters 12–14 makes it much easier to interpret what these more advanced functions are doing under the hood.

Summary

In this appendix you:

  • saw how Pingouin fits into the PyStatsV1 ecosystem as a higher-level, psychology-friendly stats package,

  • learned how to install and update Pingouin in a modern Python environment,

  • connected the Chapter 14 manual repeated-measures ANOVA to Pingouin’s rm_anova(),

  • and previewed how Pingouin can help with mixed ANOVA and more advanced analyses in later chapters.

The big picture:

  • PyStatsV1 scripts and hand calculations teach you why repeated-measures designs and ANOVAs work the way they do.

  • Pingouin shows you how professional data scientists and quantitative psychologists actually run these analyses in code.

Both perspectives are valuable. Together, they prepare you to read modern research articles, run your own studies, and move smoothly between psychology-focused tools and the broader Python data-science ecosystem.